In [1]}, a non-parametric variation of CPH called DeepSurv is proposed as a treatment recommendation system. DeepSurv uses an MLP network for characterizing the effects of a patient’s covariates on their hazard rate. This solves the parametric assumptions of the hazard function in the original CPH model. It also leads to more flexibility of DeepSurv compared to CPH. As a result, DeepSurv outperforms other CPH-based models and it can learn complex relationships between an individual’s covariates and the effect of a treatment. DeepCox [2]} proposes Deep Cox Mixtures (DCMs) for survival analysis, which generalizes the proportional hazards assumption via a mixture model, by assuming that there are latent groups and within each, the proportional hazards assumption holds. DCM allows the hazard ratio in each latent group, as well as the latent group membership, to be flexibly modeled by a deep neural network. However, both DeepSurv and DeepCox models still suffer from the same strong assumption of proportional hazards as the original CPH formulation. Also, neither of those two models supports longitudinal measurements.
